Question: Rewrite as a simplified fraction. ${0.41\overline{6} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 416.6666...\\ 100x &= 41.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 375}$ ${x = \dfrac{375}{900}} $ ${x = \dfrac{5}{12}} $